.TH  CGTRFS 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " 
.SH NAME
CGTRFS - the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
.SH SYNOPSIS
.TP 19
SUBROUTINE CGTRFS(
TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2,
IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
INFO )
.TP 19
.ti +4
CHARACTER
TRANS
.TP 19
.ti +4
INTEGER
INFO, LDB, LDX, N, NRHS
.TP 19
.ti +4
INTEGER
IPIV( * )
.TP 19
.ti +4
REAL
BERR( * ), FERR( * ), RWORK( * )
.TP 19
.ti +4
COMPLEX
B( LDB, * ), D( * ), DF( * ), DL( * ),
DLF( * ), DU( * ), DU2( * ), DUF( * ),
WORK( * ), X( LDX, * )
.SH PURPOSE
CGTRFS improves the computed solution to a system of linear
equations when the coefficient matrix is tridiagonal, and provides
error bounds and backward error estimates for the solution.

.SH ARGUMENTS
.TP 8
TRANS   (input) CHARACTER*1
Specifies the form of the system of equations:
.br
= \(aqN\(aq:  A * X = B     (No transpose)
.br
= \(aqT\(aq:  A**T * X = B  (Transpose)
.br
= \(aqC\(aq:  A**H * X = B  (Conjugate transpose)
.TP 8
N       (input) INTEGER
The order of the matrix A.  N >= 0.
.TP 8
NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.
.TP 8
DL      (input) COMPLEX array, dimension (N-1)
The (n-1) subdiagonal elements of A.
.TP 8
D       (input) COMPLEX array, dimension (N)
The diagonal elements of A.
.TP 8
DU      (input) COMPLEX array, dimension (N-1)
The (n-1) superdiagonal elements of A.
.TP 8
DLF     (input) COMPLEX array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by CGTTRF.
.TP 8
DF      (input) COMPLEX array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
.TP 8
DUF     (input) COMPLEX array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.
.TP 8
DU2     (input) COMPLEX array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.
.TP 8
IPIV    (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i).  IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.
.TP 8
B       (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.
.TP 8
LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).
.TP 8
X       (input/output) COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CGTTRS.
On exit, the improved solution matrix X.
.TP 8
LDX     (input) INTEGER
The leading dimension of the array X.  LDX >= max(1,N).
.TP 8
FERR    (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j).  The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
.TP 8
BERR    (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in
any element of A or B that makes X(j) an exact solution).
.TP 8
WORK    (workspace) COMPLEX array, dimension (2*N)
.TP 8
RWORK   (workspace) REAL array, dimension (N)
.TP 8
INFO    (output) INTEGER
= 0:  successful exit
.br
< 0:  if INFO = -i, the i-th argument had an illegal value
.SH PARAMETERS

ITMAX is the maximum number of steps of iterative refinement.
